Ko began with an even-par 72 yesterday, which left her in contention in the early stages, but the task of overhauling this deficit may be too great for her during the next two rounds.
Martin, the world No 99 who has never won on the LPGA Tour, showed impressive control to navigate the tricky course in Southport, England and was the only player to shoot under 70 in both opening rounds.
"It's been a fun day," Martin told local media. "It's always nice when your plan pans out. Earlier in the week my caddy and I worked out where the widest parts of the fairway were and where I would have the best approaches into the greens and those are what we have been aiming at."
Martin has a three-shot lead over Spain's Beatriz Recari and Korea's So Yeon Ryu who are both at three-under.
American Michelle Wie, who won last month's Women's US Open, was among the big names to miss the cut after rounds of 75 and 78.
"I'm extremely disappointed how I played," she told reporters. "But, you know, there's nothing I can do about it. I'm just going to think about what I did wrong here and see how I can improve."
Kiwi Cathryn Bristow, who began with a horror 13-over 85 yesterday, only gradually improved in her second-round with a 10-over 82 as she also missed the cut.